Here's a question from the OG 12 that I was able to solve, albeit inefficiently. And the OG solution doesn't make sense to me, so I'd really appreciate anyone's shortcut tips!
Pg 259, Quest 220:
A part-time employee whose hourly wage was increased by 25% decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced?
A 12.5%
B 20%
C 25%
D 50%
E 75%
I plugged in an imaginary wage and work week and solved from there. If the employee was previously paid $10/hour and worked 40 hours a week, he made $400 a week. His raise set him at $12.50/hour, and if he wanted to reduce his hours and earn the same amount, then 12.5x = 400 and x = 8. The final step is to solve for the percentage 2/10, which is 20%.
The OG solves algebraically, though:
1.25wH = wh
Both sides divided by w for:
1.25H = h
But then it says:
H= 0.8h
Seems like a much quicker formula, but where does the 0.8 come from?
Thanks!
Matthew
Pg 259, Quest 220:
A part-time employee whose hourly wage was increased by 25% decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced?
A 12.5%
B 20%
C 25%
D 50%
E 75%
I plugged in an imaginary wage and work week and solved from there. If the employee was previously paid $10/hour and worked 40 hours a week, he made $400 a week. His raise set him at $12.50/hour, and if he wanted to reduce his hours and earn the same amount, then 12.5x = 400 and x = 8. The final step is to solve for the percentage 2/10, which is 20%.
The OG solves algebraically, though:
1.25wH = wh
Both sides divided by w for:
1.25H = h
But then it says:
H= 0.8h
Seems like a much quicker formula, but where does the 0.8 come from?
Thanks!
Matthew
